Choukri DERBAZİ, Zidane BAİTİCHE, Mouﬀak BENCHOHRA

Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the $\psi $--Caputo fractional derivative in Banach spaces. Our approach is based on a new fixed point theorem with respect to convex-power condensing operator combined with the technique of measures of noncompactness. Finally, two examples are given to illustrate the obtained results.

Keywords:

$\psi $--Caputo fractional derivative, Cauchy problem, convex-power condensing operator fixed point theorem, Banach spaces, measures of noncompactness,

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